Comments on Holographic Entanglement Entropy and RG Flows

TL;DR

This paper investigates holographic entanglement entropy to define a c-function in various dimensions, demonstrating its monotonic decrease under certain conditions in Einstein gravity and exploring phase transitions in entanglement entropy for holographic RG flows.

Contribution

It introduces a candidate c-function based on holographic entanglement entropy and analyzes its monotonicity and phase transition behavior across different gravity theories.

Findings

The c-function decreases monotonically along RG flows in Einstein gravity when null energy condition holds.

In Gauss-Bonnet gravity, the monotonicity of the c-function is not guaranteed.

Entanglement entropy can undergo phase transitions, causing discontinuous changes in the c-function.

Abstract

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a 'phase transition' as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.